 Surprising non-scaling behavior in fractional diffusionB.N.Narahari Achar and John W. Hanneken Physica A: Statistical Mechanics and its Applications, 2003, vol. 322, issue C, 195-200 Abstract: It is well known that Brownian diffusion is characterized by a mean-squared displacement which varies linearly in time, 〈r2〉∼t and that anomalous diffusion, by a mean-square displacement which is nonlinear in time, 〈r2〉∼tα. It is generally accepted that fractional diffusion, which is used to describe anomalous diffusion, is also characterized by the same scaling behavior in the second moment, 〈r2〉∼tα. It is shown in this paper that this is not always so and that inward radial fractional diffusion in one, two and three dimensions does not exhibit this scaling, where as outward radial fractional diffusion in these cases does exhibit the scaling. The reason for this unexpected behavior is the existence of a characteristic length, and the separation of variables, which occurs because of the boundary conditions. Keywords: Fractional diffusion; Anomalous diffusion; tα-scaling (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:322:y:2003:i:c:p:195-200 DOI: 10.1016/S0378-4371(02)01911-8 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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